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Positive Definite Solutions of the Nonlinear Matrix Equation X+A~*X~qA=Q(q>O)

Author: XieWeiWei
Tutor: ZhangGuoFeng
School: Lanzhou University
Course: Computational Mathematics
Keywords: Nonlinear matrix equation Hermitian positive definite solution Iterative method Fixed point theorem
CLC: O241.6
Type: Master's thesis
Year: 2011
Downloads: 28
Quote: 0
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Abstract


Nonlinear matrix equation solving algebra problems in recent years, the field of numerical analysis and nonlinear field study and explore one of the important issues . Nonlinear matrix equation in control theory , dynamic programming , statistics, random infiltration ladder networks have important applications in many fields . This paper discusses the nonlinear matrix equation XA * XqA = Q (q gt; 0) is positive definite solution of the existence of an iterative method is given , where A is , n × n complex matrix , Q is n × n order positive definite matrix . The first part describes the nonlinear matrix equation development and research background and the main results of the study and describes the notation used in this article . The second part discusses the equation XA * XqA = Q (q gt; 0) properties of solutions and Hermitian positive definite solution obtained sufficient conditions for the existence . The third part gives a nonlinear matrix equation x A * XqA = Q (q gt; 0) is positive definite solution effective iterative method and prove the convergence of iterative methods . Then on the solution perturbation analysis are discussed. The fourth section presents a numerical example. Numerical examples demonstrate the use of paper, the correctness of the conclusions and solving method.

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